The Wiener index of a connected graph G, denoted by W (G), is defined as 12 ∑ u,v∈V (G) dG(u, v). Similarly, the hyper-Wiener index of a connected graph G, denoted by WW (G), is defined as 1 2W (G) + 1 4 ∑ u,v∈V (G) dG(u, v). The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, ...

Based on the Mendia and Sarkar's algorithm [8], we propose an optimal and nonredundant distributed broadcasting algorithm in star graphs. For an n-dimensional star graph, our algorithm takes O( n log, n ) time and guarantees that all nodes in the star graph receive the message exactly once. Moreover, broadcasting m packets in a pipeline fashion takes O( m log, n + n log, n ) time due to the non...

In this survey the concept of hyperedge replacement is presented as an elementary approach to graph and hypergraph generation. In particular, hyperedge replacement graph grammars are discussed as a (hyper)graph-grammatical counterpart to context-free string grammars. To cover a large part of the theory of hyperedge replacement, structural properties and decision problems, including the membersh...

The hyper-Zagreb index of a connected graph G, denoted by HM(G), is defined as HM(G) = ∑ uv∈E(G) [dG(u) + dG(v)] where dG(z) is the degree of a vertex z in G. In this paper, we study the hyper-Zagreb index of four operations on graphs.

In this paper we present an algorithm for layout and visualization of music collections based on similarities between musical artists. The core of the algorithm consists of a non-linear low dimensional embedding of a similarity graph constrained to the surface of a hyper-sphere. This approach effectively uses additional dimensions in the embedding. We derive the algorithm using a simple energy ...